GCF of 22/60, 64/30, 19/67, 54/78
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 22/60, 64/30, 19/67, 54/78 i.e 1/52260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 22/60, 64/30, 19/67, 54/78.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 22/60,64/30,19/67,54/78?
Given fractions are 22/60,64/30,19/67,54/78
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 22/60,64/30,19/67,54/78, numerators are 22,64,19,54
Denominators are 60,30,67,78
The GCF of 22,64,19,54 is 1 .
LCM of 60,30,67,78 is 52260.
The greatest common factor of 22/60,64/30,19/67,54/78 = [GCF of 22,64,19,54]/[LCM of 60,30,67,78]= 1/52260
Therefore, the GCF of 22/60,64/30,19/67,54/78 is 1/52260.
To find the highest common factor of 22,64,19,54, we have to find the factors of both numbers and list the highest common factor.
The factors of 22 are 1, 2, 11, 22
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 19 are 1, 19
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The HCF of 22,64,19,54 is 1.
Lets's calculate GCF of 22,64,19,54
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 22,64,19,54 By Matching Biggest Common Factor Method
Now, list down the factors of 22
:1,2,11,22
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 19
:1,19
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Greatest Common Factor
We found the factors 22,64,19,54 . The biggest common factor number is the GCF number.
So the greatest common factor 22,64,19,54 is 1.
Lets's calculate LCM of 60,30,67,78
| 2 | 60, 30, 67, 78 |
| 3 | 30, 15, 67, 39 |
| 5 | 10, 5, 67, 13 |
| 2, 1, 67, 13 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 2 x 1 x 67 x 13 = 52260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/52260
Therefore, the GCF of Fractions 22/60,64/30,19/67,54/78 is 1/52260
Least Common Multiple of 60,30,67,78 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 60,30,67,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,30,67,78) = 1
common factors(in case of two or more numbers have common factors) = 180
GCF(60,30,67,78) x common factors =1 x 180 = 180
LCM(60,30,67,78) = ( 60 × 30 × 67 × 78 ) / 180
LCM(60,30,67,78) = 9406800 / 180
LCM(60,30,67,78) = 52260
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 22/60, 64/30, 19/67, 54/78
1. What is the HCF of 22,64,19,54?
The HCF of 22,64,19,54 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 22/60, 64/30, 19/67, 54/78?
Answer: GCF of Numerators as per given numbers 22/60, 64/30, 19/67, 54/78 is
GCF of Numerators i.e. for 22,64,19,54 is 1
LCM of denominators i.e. for 60,30,67,78 is 52260.
Thus, GCF of Fractions is 1/52260.Finally, GCF of Fractions for 22/60, 64/30, 19/67, 54/78 is 1/52260.